1

Statistical Model Analysis of K/ and p/ fluctuations in heavy-ion collisions付菁华

华中师范大学 粒子物理研究所

2

Motivation – Fluctuations & Phase Transition

TV

kT

N

N

2

2 )(

Particle Number Fluctuations in the Grand Canonical Ensemble

• Relative Fluctuations ~ V-1 Negligible

• Phase Transitions

NT

T p

V

V,

1

Unusually Large Fluctuations

3

Motivation – Thermal Model & Particle Ratios

The Statistical Model very successful in describing particle yield ratios in nucleus - nucleus collisions

Whether the hadronic statistical model is equally well in describing particle yield fluctuations ?

4

K/ Fluctuations & Energy Dependence

Strong Energy Dependence

Large Fluctuations ？

5

Particle ratio fluctuations

ondistributi /

theofdeviation standard the: )/(

eventan in

(2) 1 typeof particles ofnumber the:)(

/

)/(

/

)/()/(

21

212

21

2

21

212

2

21

212

21

NN

NN

NN

NN

NN

NN

NNNN stat

dyn

ratios of particles volume fluctuations cancel

K/ fluctuations : N1 － number of kaons in an event N2 － number of pions in an event

6

Statistical model

isiIibi

iii

iiii

iii

SIB

TEn

nnpd

VgN

npd

VgN

3

3

32

3

3

3

1]/)exp[(

1

)1()2(

)(

)2(

RRjiRRjRiRjiji

RRiRii

nnNnnNNNNN

nNNN

2**

*

Upper sign for frmions, lower sign for bosons

NN 2

<0 FD

=0 MB

>0 BE

7

Model Parameters

GeVNET

sGeVGeV

s

BQ

NN

NNb

s

I

1/ :

)273.01/(308.1

)(

onconservati sstrangenes :

4.0/ :

1

3

How about volume V ?

Not needed for N1/N2

8

Volume

VNN

NN

NN

NNNN

VNN

N

statdyn

ii

i

1

)/(

)/(

)/(

)/()/(

11

221

212

221

212

21

2

2

From Ref. Nucl.Phys.A 772 (2006) 167, in unit of fm3

9

Correction NA49 3D acceptance table

HIJING simulations

The percentage of particles inside the NA49

acceptance table

Decreasing Acceptance

10

Correction STAR

dydN

dmdydmm

Ndp

pPPp

cGeVp

T

T

m

m TTT

T

PTT

T

/

2)(

yields corrected

yields measured

])/(exp[ )( : efficiency tracking

1|| , /6.02.0 : cuts kinematic

22

22

2

6.0

2.0

2

10

11

Results ─ Energy Dependence

Data :Full symbols:

Model :Open symbols connected with lines:

12

Data :Full symbols: Model :Open symbols:

KK

KK

KKK

and:opposite

and:same

:/

Results ─ Centrality Dependence

13

Conclusion

Detector acceptance → increase of K/ fluctuations at the lower NA49 energies

Kinematic cuts & tracking efficiency → good description of most central STAR K/

fluctuations & its centrality dependence

Thank you !

14

15

16

Particle ratio fluctuations

jiji

iii

stat

NNNNNN

NNN

NNNN

NN

NN

NN

N

N

N

N

NN

NN

21

222

212

21

212

21

212

2

22

2

1

21

221

212

11

)/(

)/(

2)/(

)/(

17

Centrality dependence

The volume parameter is decided by asking

the average number of K- in the model the

same as the STAR measured K- integrated

rapidity density